All readings will be listed here, organized by topic. Dates indicate the class by which you should have read the indicated material.   Some readings may be announced here before they are announced in class, in case you want to read ahead.   Sometimes, particularly if I am traveling, you may find some references posted at the library class reserves before they are linked here.
If a reading does not have a date, you don't have to worry about it yet.

Fundamentals of Probability Theory and Stochastic Processes

Assigned Readings

• Karlin & Taylor, A First Course in Stochastic Processes, Sec. 1.1A-F (PDF) (01/22/04)
• Kloeden & Platen, Numerical Solution of Stochastic Differential Equations, Sec. 1.1-1.3 (PDF) (01/22/04)
• missing pages have been included
• Risken, The Fokker-Planck Equation, Secs. 2.2 and 2.3,  (PDF) (01/29/04)
• This summarizes cumulants and generating functions.
• Kloeden & Platen, Numerical Solution of Stochastic Differential Equations, Sec. 1.4 (PDF) (02/09/04)

Optional Readings

• Kloeden & Platen, Numerical Solution of Stochastic Differential Equations, Sec. 2.1-2.2 (PDF)
• Brief overview of the connections between measure theory and probability.  The copy is rather poor; I will try to replace it.

Finite-State, Discrete-Time Markov Chains

Assigned Readings

Lawler, Intoduction to Stochastic Processes, Ch. 1 (PDF) (03/08/04)

Optional Readings

• Resnick, Adventures in Stochastic Processes, Secs. 2.12-2.15 (PDF)
• Complete proof of existence and uniqueness of stationary distribution, and law of large numbers for Markov chains. Also some further discussion of recurrence/transience classification techniques and computational techniques for stationary distribution.
• Karlin & Taylor, A First Course in Stochastic Processes, App. 2 (PDF)
• Perron-Frobenius theory for positive matrices
• Haken, Synergetics, Secs. 4.6-4.8  (PDF)
• Stationary distributions:  Detailed balance, microreversibility, and Kirchoff's method of solution
• Guttorp, Stochastic Modeling of Scientific Data, Sec. 2.1 (PDF)
• Maximum likelihood method for choosing parameters in Markov chain
• Bhat & Miller, Elements of Applied Stochastic Processes, Sec. 2.1 & 2.6 (PDF)
• Method for calculating variance of first hitting times, and application to delinquent credit management
• Resnick, Adventures in Stochastic Processes, Secs. 2.5-2.6 (PDF)
• Dissection principle for Markov chains and some theory on recurrence and transience when the n-step probability transition densities can be computed explicitly.

Countable State, Discrete-Time Markov Chains

Assigned Readings

Lawler, Intoduction to Stochastic Processes, Ch. 2 (PDF) (03/25/04)

Karlin & Taylor, A First Course in Stochastic Processes, Ch. 2 and 3 (PDF) (03/22/04)

Countable State, Continuous-Time Markov Chains

Assigned Readings

Lawler, Intoduction to Stochastic Processes, Ch. 3 (PDF)  (04/01/04)

Andersson and Britton, Stochastic Epidemic Models and Their Statistical Analysis, Ch. 2 (PDF) (04/12/04)

Optional Readings

• Reichl, A Modern Course in Statistical Physics, Ch. 5 (PDF) (PDF file may still be corrupted)
• A concise discussion of Markov chains and stochastic differential equations from a physicist's perspective.  A nice collection of concepts, but there are some misleading statements!

Martingales

Assigned Readings

Karlin & Taylor, A First Course in Stochastic Processes, Sec. 6.1-6.4 (PDF) (04/12/04)

Continuous Space, Continuous-Time Markov Processes

Assigned Readings

Kloeden and Platen, Numerical Solution of Stochastic Differential Equations, Sec. 1.7,1.8 (PDF) (04/19/04)

Kloeden and Platen, Numerical Solution of Stochastic Differential Equations, Sec. 2.3,2.4 (PDF) (04/22/04)

Optional Readings

Friedman, Stochastic Differential Equations and Applications, Ch. 2

Stochastic Calculus

Assigned Readings

Kloeden and Platen, Numerical Solution of Stochastic Differential Equations, Ch. 3 (PDF) (04/30/04)

Stochastic Differential Equations

Optional Readings

Kloeden and Platen, Numerical Solution of Stochastic Differential Equations, Ch. 4.1, 4.5, 4.6, 4.8, 4.9 (PDF)

Kloeden and Platen, Numerical Solution of Stochastic Differential Equations, Ch. 6.1, 6.3  (PDF)

Numerical Solution of Stochastic Differential Equations

Assigned Readings

Higham, "An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations," SIAM Review 43 (3),  525-546 (2001)

Financial Derivatives and Partial Differential Equations

Optional Readings

Almgren, "Financial Derivatives and Partial Differential Equations," American Mathematical Monthly 109 (1),  1-12 (2002)